Point Slope Word Problems

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by the formula: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you identify the slope from a point-slope equation?

Back

In the point-slope equation y - y_1 = m(x - x_1), the slope m is the coefficient of (x - x_1).

Front

What does the slope represent in a real-world context?

Back

The slope represents the rate of change between two variables. For example, in a business context, it could represent profit per item sold.

Front

How can you convert a point-slope equation to slope-intercept form?

Back

To convert from point-slope form (y - y_1 = m(x - x_1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of the point (x_1, y_1) in the point-slope form?

Back

The point (x_1, y_1) is a specific point on the line, which helps to define the line's position in the coordinate plane.

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that for every 1 unit increase in x, y decreases by 3 units, meaning the line descends from left to right.

Front

How do you determine if a point lies on a line represented by a point-slope equation?

Back

To determine if a point (x, y) lies on the line, substitute x into the equation and check if the resulting y equals the y-coordinate of the point.

Front

What is the first step in solving a point-slope word problem?

Back

The first step is to identify the slope and a point from the problem context.

Front

How do you write a point-slope equation from a word problem?

Back

Extract the slope and a point from the problem, then use the point-slope formula: y - y_1 = m(x - x_1).

Front

What is the meaning of a positive slope in a real-world scenario?

Back

A positive slope indicates that as one variable increases, the other variable also increases, showing a direct relationship.